Abstract

The distribution of polarization in the overcast sky has been practically unknown. Earlier the polarization of light from heavily overcast skies (when the Sun’s disc was invisible) has been measured only sporadically in some celestial points by point-source polarimetry. What kind of patterns of the degree p and angle α of linear polarization of light could develop after transmission through a thick layer of ice or water clouds? To answer this question, we measured the p and α patterns of numerous totally overcast skies on the Arctic Ocean and in Hungary by full-sky imaging polarimetry. We present here our finding that depending on the optical thickness of the cloud layer, the pattern of α of light transmitted through the ice or water clouds of totally overcast skies is qualitatively the same as the α pattern of the clear sky. Under overcast conditions the value of α is determined predominantly by scattering on cloud particles themselves. Nevertheless, the degrees of linear polarization of light from overcast skies were rather low (p16%). Our results obtained under overcast conditions complete the earlier findings that the α pattern of the clear sky also appears in partly cloudy, foggy, and smoky skies. Our results show that the celestial distribution of the direction of polarization is a very robust pattern being qualitatively always the same under all possible sky conditions. This is of great importance for the orientation of polarization-sensitive animals based on sky polarization under conditions when the Sun is not visible.

© 2007 Optical Society of America

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References

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  1. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
    [CrossRef]
  5. I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
    [PubMed]
  6. B. Suhai and G. Horváth, "How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study," J. Opt. Soc. Am. A 21, 1669-1676 (2004).
    [CrossRef]
  7. R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
    [CrossRef]
  8. R. Hegedüs, S. Åkesson, and G. Horváth, "Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?" Appl. Opt. 46, 2717-2726 (2007).
    [CrossRef] [PubMed]
  9. G. P. Können, Polarized Light in Nature (Cambridge U. Press, l985).
  10. G. Horváth and D. Varjú, Polarized Light in Animal Vision--Polarization Patterns in Nature (Springer-Verlag, 2003).
  11. K. L. Coulson, "On the solar radiation field in a polluted atmosphere," J. Quant. Spectrosc. Radiat. Transf. 2, 739-755 (1971).
    [CrossRef]
  12. M. L. Brines and J. L. Gould, "Skylight polarization patterns and animal orientation," J. Exp. Biol. 96, 69-91 (1982).
  13. J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. I," Philos. Mag. 41, 107-120 (1871).
  14. J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. II," Philos. Mag. 41, 274-279 (1871).
  15. N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
    [CrossRef]
  16. K. Bullrich, R. Eiden, and W. Nowak, "Sky radiation, polarization, and twilight radiation in Greenland," Pure Appl. Geophys. 64, 220-242 (1966).
    [CrossRef]
  17. W. W. Cochran, H. Mouritsen, and M. Wikelski, "Migrating songbirds recalibrate their magnetic compass daily from twilight cues," Science 304, 405-408 (2004).
    [CrossRef] [PubMed]
  18. K. P. Able and M. Able, "The flexible migratory orientation system of the Savannah sparrow (Passerculus sandwichensis)," J. Exp. Biol. 199, 3-8 (1996).
    [PubMed]
  19. R. Muheim, J. B. Phillips, and S. Åkesson, "Polarized light cues underlie compass calibration in migratory songbirds," Science 313, 837-839 (2006).
    [CrossRef] [PubMed]

2007 (2)

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
[CrossRef]

R. Hegedüs, S. Åkesson, and G. Horváth, "Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?" Appl. Opt. 46, 2717-2726 (2007).
[CrossRef] [PubMed]

2006 (1)

R. Muheim, J. B. Phillips, and S. Åkesson, "Polarized light cues underlie compass calibration in migratory songbirds," Science 313, 837-839 (2006).
[CrossRef] [PubMed]

2004 (3)

B. Suhai and G. Horváth, "How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study," J. Opt. Soc. Am. A 21, 1669-1676 (2004).
[CrossRef]

N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
[CrossRef]

W. W. Cochran, H. Mouritsen, and M. Wikelski, "Migrating songbirds recalibrate their magnetic compass daily from twilight cues," Science 304, 405-408 (2004).
[CrossRef] [PubMed]

2001 (2)

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
[CrossRef]

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

1997 (2)

1996 (1)

K. P. Able and M. Able, "The flexible migratory orientation system of the Savannah sparrow (Passerculus sandwichensis)," J. Exp. Biol. 199, 3-8 (1996).
[PubMed]

1982 (1)

M. L. Brines and J. L. Gould, "Skylight polarization patterns and animal orientation," J. Exp. Biol. 96, 69-91 (1982).

1971 (1)

K. L. Coulson, "On the solar radiation field in a polluted atmosphere," J. Quant. Spectrosc. Radiat. Transf. 2, 739-755 (1971).
[CrossRef]

1966 (1)

K. Bullrich, R. Eiden, and W. Nowak, "Sky radiation, polarization, and twilight radiation in Greenland," Pure Appl. Geophys. 64, 220-242 (1966).
[CrossRef]

1871 (2)

J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. I," Philos. Mag. 41, 107-120 (1871).

J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. II," Philos. Mag. 41, 274-279 (1871).

Able, K. P.

K. P. Able and M. Able, "The flexible migratory orientation system of the Savannah sparrow (Passerculus sandwichensis)," J. Exp. Biol. 199, 3-8 (1996).
[PubMed]

Able, M.

K. P. Able and M. Able, "The flexible migratory orientation system of the Savannah sparrow (Passerculus sandwichensis)," J. Exp. Biol. 199, 3-8 (1996).
[PubMed]

Åkesson, S.

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
[CrossRef]

R. Hegedüs, S. Åkesson, and G. Horváth, "Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?" Appl. Opt. 46, 2717-2726 (2007).
[CrossRef] [PubMed]

R. Muheim, J. B. Phillips, and S. Åkesson, "Polarized light cues underlie compass calibration in migratory songbirds," Science 313, 837-839 (2006).
[CrossRef] [PubMed]

Bréon, F.-M.

N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
[CrossRef]

Brines, M. L.

M. L. Brines and J. L. Gould, "Skylight polarization patterns and animal orientation," J. Exp. Biol. 96, 69-91 (1982).

Bullrich, K.

K. Bullrich, R. Eiden, and W. Nowak, "Sky radiation, polarization, and twilight radiation in Greenland," Pure Appl. Geophys. 64, 220-242 (1966).
[CrossRef]

Cochran, W. W.

W. W. Cochran, H. Mouritsen, and M. Wikelski, "Migrating songbirds recalibrate their magnetic compass daily from twilight cues," Science 304, 405-408 (2004).
[CrossRef] [PubMed]

Coulson, K. L.

K. L. Coulson, "On the solar radiation field in a polluted atmosphere," J. Quant. Spectrosc. Radiat. Transf. 2, 739-755 (1971).
[CrossRef]

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).

Duggin, M. J.

Eiden, R.

K. Bullrich, R. Eiden, and W. Nowak, "Sky radiation, polarization, and twilight radiation in Greenland," Pure Appl. Geophys. 64, 220-242 (1966).
[CrossRef]

Gál, J.

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
[CrossRef]

Gould, J. L.

M. L. Brines and J. L. Gould, "Skylight polarization patterns and animal orientation," J. Exp. Biol. 96, 69-91 (1982).

Hegedüs, R.

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
[CrossRef]

R. Hegedüs, S. Åkesson, and G. Horváth, "Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?" Appl. Opt. 46, 2717-2726 (2007).
[CrossRef] [PubMed]

Horváth, G.

R. Hegedüs, S. Åkesson, and G. Horváth, "Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?" Appl. Opt. 46, 2717-2726 (2007).
[CrossRef] [PubMed]

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
[CrossRef]

B. Suhai and G. Horváth, "How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study," J. Opt. Soc. Am. A 21, 1669-1676 (2004).
[CrossRef]

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
[CrossRef]

G. Horváth and D. Varjú, Polarized Light in Animal Vision--Polarization Patterns in Nature (Springer-Verlag, 2003).

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, l985).

Liu, Y.

Meyer-Rochow, V. B.

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
[CrossRef]

Mouritsen, H.

W. W. Cochran, H. Mouritsen, and M. Wikelski, "Migrating songbirds recalibrate their magnetic compass daily from twilight cues," Science 304, 405-408 (2004).
[CrossRef] [PubMed]

Muheim, R.

R. Muheim, J. B. Phillips, and S. Åkesson, "Polarized light cues underlie compass calibration in migratory songbirds," Science 313, 837-839 (2006).
[CrossRef] [PubMed]

North, J. A.

Nowak, W.

K. Bullrich, R. Eiden, and W. Nowak, "Sky radiation, polarization, and twilight radiation in Greenland," Pure Appl. Geophys. 64, 220-242 (1966).
[CrossRef]

Phillips, J. B.

R. Muheim, J. B. Phillips, and S. Åkesson, "Polarized light cues underlie compass calibration in migratory songbirds," Science 313, 837-839 (2006).
[CrossRef] [PubMed]

Pomozi, I.

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Schutgens, N. A. J.

N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
[CrossRef]

Stammes, P.

N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
[CrossRef]

Strutt, J. W.

J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. I," Philos. Mag. 41, 107-120 (1871).

J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. II," Philos. Mag. 41, 274-279 (1871).

Suhai, B.

Tilstra, L. G.

N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
[CrossRef]

Varjú, D.

G. Horváth and D. Varjú, Polarized Light in Animal Vision--Polarization Patterns in Nature (Springer-Verlag, 2003).

Voss, K. J.

Wehner, R.

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
[CrossRef]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
[CrossRef]

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Wikelski, M.

W. W. Cochran, H. Mouritsen, and M. Wikelski, "Migrating songbirds recalibrate their magnetic compass daily from twilight cues," Science 304, 405-408 (2004).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Exp. Biol. (3)

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

M. L. Brines and J. L. Gould, "Skylight polarization patterns and animal orientation," J. Exp. Biol. 96, 69-91 (1982).

K. P. Able and M. Able, "The flexible migratory orientation system of the Savannah sparrow (Passerculus sandwichensis)," J. Exp. Biol. 199, 3-8 (1996).
[PubMed]

J. Geophys. Res. (1)

N. A. J. Schutgens, L. G. Tilstra, P. Stammes, and F.-M. Bréon, "On the relationship between Stokes parameters Q and U of atmospheric ultraviolet/visible/near-infrared radiation," J. Geophys. Res. 109, D09205, doi: 10.1029/2003JD004081 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transf. (1)

K. L. Coulson, "On the solar radiation field in a polluted atmosphere," J. Quant. Spectrosc. Radiat. Transf. 2, 739-755 (1971).
[CrossRef]

Philos. Mag. (2)

J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. I," Philos. Mag. 41, 107-120 (1871).

J. W. Strutt (Lord Rayleigh), "On the light from the sky, its polarisation and colour. II," Philos. Mag. 41, 274-279 (1871).

Proc. R. Soc. London, Ser. A (2)

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, "Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies," Proc. R. Soc. London, Ser. A 463, 1081-1095 (2007).
[CrossRef]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, "Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle," Proc. R. Soc. London, Ser. A 457, 1385-1399 (2001).
[CrossRef]

Pure Appl. Geophys. (1)

K. Bullrich, R. Eiden, and W. Nowak, "Sky radiation, polarization, and twilight radiation in Greenland," Pure Appl. Geophys. 64, 220-242 (1966).
[CrossRef]

Science (2)

W. W. Cochran, H. Mouritsen, and M. Wikelski, "Migrating songbirds recalibrate their magnetic compass daily from twilight cues," Science 304, 405-408 (2004).
[CrossRef] [PubMed]

R. Muheim, J. B. Phillips, and S. Åkesson, "Polarized light cues underlie compass calibration in migratory songbirds," Science 313, 837-839 (2006).
[CrossRef] [PubMed]

Other (3)

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).

G. P. Können, Polarized Light in Nature (Cambridge U. Press, l985).

G. Horváth and D. Varjú, Polarized Light in Animal Vision--Polarization Patterns in Nature (Springer-Verlag, 2003).

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Figures (4)

Fig. 1
Fig. 1

Color picture (A) and patterns of the radiance I (B–D), degree of linear polarization p (E–G), and angle of polarization α measured clockwise from the local meridian (H–J) of the Arctic clear sky S0 (Table 1) measured by full-sky imaging polarimetry in the red ( 650 nm ) , green ( 550 nm ) , and blue ( 450 nm ) parts of the spectrum. The optical data of this sky are given in Table 2. The optical axis of the fisheye lens was vertical; thus the horizon is the perimeter and the center of the circular patterns is the zenith. On the bottom of the circular color picture the silhouette of the Swedish icebreaker Oden can be seen. In A the position of the sun near the horizon is marked by a gray dot (orange online) and in the α patterns (H–J) the positions of the Arago and Babinet neutral (unpolarized) points are marked by white dots with black perimeters.

Fig. 2
Fig. 2

Same as Fig. 1 but for the totally overcast sky S9, the data of which are given in Tables 1, 2. On the periphery of the color picture the dark silhouette of some trees can be seen.

Fig. 3
Fig. 3

Color pictures and patterns of the angle of polarization α (measured clockwise from the local meridian) of Arctic and Hungarian total overcast skies S1–S15, the data of which are given in Tables 1, 2. The α patterns were measured by full-sky imaging polarimetry in the blue ( 450 nm ) part of the spectrum. Quite similar α patterns were obtained in both the green and red spectral ranges.

Fig. 4
Fig. 4

A, Color picture of a foggy sky with the visible Sun’s disc. B, Pattern of the angle of polarization α if the radiance values of all pixels in all three polarization pictures (taken with three different directions of the transmission axis of the linear polarizer) are multiplied by factors f 1 = f 2 = f 3 = 1 . C, The α pattern is artificially rotated if the value of f 1 is increased from 1.00 to 1.15, for example.

Tables (2)

Tables Icon

Table 1 Date, Time, Geographical Coordinates, Solar Elevation Angle, and Weather and Surface Conditions during Full-Sky Imaging Polarimetric Measurements Performed in the High Arctic (Skies S0–S8) and Hungary (S9–S15) a, b

Tables Icon

Table 2 Optical Characteristics of Clear and Totally Overcast Skies Measured by Full-Sky Imaging Polarimetry in the Red ( 650 nm ) , Green ( 550 nm ) , and Blue ( 450 nm ) Parts of the Spectrum a

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